Jon & all, Re Bob Scott: So single direction terminations at agraff and capo wouldn't= cause false beats by virtue of not being on the sound production end of the= string huh? OK, fair enough, but I just went out in the shop for more= ammunition. I've got a Baldwin SF ready to go with re-notched bridges, new= bridge pins (CA'd in) sounds clean and nice (except for final tuning) from= one end to the other. OK, here goes. With back lighting along the strings,= it's obvious that the string excursion is not purely vertical. They go all= over the place without false beats. Doesn't compute. I'm still holding out= for the loose bridge pin theory because with the string stuck off the= bridge, you wouldn't have the horizontal motion anchor of the bridge= surface allowing the pin to flex in a loose hole with the horizontal phase= of string excursion. Seating the string on the bridge would help in the= cases where the resulting horizontal friction overcomes the leverage of= horizontal string movement. What do you think? Regards, Ron Nossaman =20 =20 At 10:43 AM 4/13/97 -0400, you wrote: >This appeared in rmmp. back in December.=20 >~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ >Bob Scott wrote: > >An easy way to understand false beats is to imagine the piano string >just after it is struck. It is vibrating essentially up and down. >But it doesn't continue to vibrate that way. It begins drifting >towards a side-to-side vibration. When it vibrates like that there is >less coupling to the sound board. Then the vibration continues to >drift to an up and down motion - this time upside down from the >original motion. Now it is producing sound 180 degrees out of phase >with what it was doing originally. If it goes through this cycle once >per second you will hear a once per second fluctuation in the loudness >of the note. It is not like vibrato, which is a fluctuation in the >pitch of a note. Now what makes the string decide to start vibrating >sideways? Lots of various imperfections in the string or its seating >can cause that. But the effect is a cyclic fluctuation in the >loudness of the note which is indistinguishable from the sound made >from two strings tuned slightly off from each other. > > -Bob Scott (rscott@wwnet.com) >~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ >At 03:39 AM 4/13/97 +0000, you wrote: >>Ron & list: >> >>I'm on my way out of town for two weeks, but this was an interesting= thread, >>and I wanted to at least give a swag, in case the thread has died by the= time I >>get back. >>Frictional force is equal to the normal force times the coefficient of >>friction (Ff=3DFn x u). I'm not a piano technician, so I will assume some >>values for discussion purposes, but I think the logic will hold. The >>downbearing force is a function of=20 >>the angle across the bridge versus the string tension. The side force >>against the bridge pin is a function of the side angle against the pin and >>the string tension. >>The string tension being a constant for a particular string the forces >>involved (down >>force versus side force against the bridge pin) are a ratio of the angles >>down and sideways on the pin. I looked at my piano and it looks like >>typical ratios would be: >>down force .1 inch down over a 30 inch length or a tangent of 1/300 versus= a >>side angle force of .1 inch sideways over a .75 inch length or a tangent= of >>1/7.5 (depending of course on what note you are looking at). Please=20 >>note that I am just wildly estimating, but the differences are so great= that >>the argument will hold with a large estimation error. Anyway..... the >>sideward force on >>the bridge pin relative to the down force will be a ratio of the above= numbers. >>In our hypothetical example above, down force would only be 7.5/300 of the >>side force on the pin. With a friction coefficient of approximately .1 to >>.15 for lubricated copper alloy versus steel, it looks like the bridge= pins >>could definitely hold a displaced string off of the bridge, even with the >>negative angle the bridge pins have. If this thread is still going when I >>get back I'll take some measurements, and can calculate the angle a bridge >>pin would have to be at to prevent this from happening. Of course a >>microscopic burr or imperfection on the pin will also lead towards causing >>the string to stay up off of the bridge when displaced. >> >>As to this causing false beats, I don't pretend to know the answer; but= will >>ask a >>naive question (I don't have any acoustic background knowledge): When the >>string is seated against the bridge it has one degree of freedom (it can >>move up and down, it seems sideways would be rapidly damped). If it is= held >>off the bridge up on the pin it can vibrate in a more 360 degree mode - >>could this cause false beats?) >> >>Well, I've got to run - please forgive me for the above "off the top of my >>head"=20 >>comments; I like to think things through more thoroughly, but wanted to >>answer before I left! >> >> Regards, Mike =20 <****** history deleted ******> Ron Nossaman
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